For men on the non formal nights in the diningroom......... is pants with a shirt and tie ok? No jacket.
The prescribed attire varies from one cruise line to another and what people actually wear on a particular line may vary from one destination to another. On Princess Cruises, all nights except the formal nights are "smart casual" -- which basically means that gentlemen wear a polo shirt, golf shirt, sports shirt, or Hawaiian shirt with slacks, socks, and dress shoes. A dress shirt and tie and a sport coat or a business suit are optional. On Celebrity Cruises, some nights are "casual" -- same as above -- and others are "informal" -- meaning that a sport coat is necessary. Your pre-cruise information package should contain more detailed information on the number of evenings for each prescribed dress and the corresponding attire.
I have observed that passengers on cruises to the Caribbean, the Mexican Riviera, and Alaska tend to be more lax in observance of the prescribed dress than passengers on cruises to other destinations. For better or for worse, these destinations seem to draw a lot of "first time" passengers who don't read the pre-cruise information very carefully and thus do not bring the proper attire.